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Let f ={(x ,(x^2)/(1+x^2)):x in R}be a f...

Let `f ={(x ,(x^2)/(1+x^2)):x in R}`be a function from R into R. Determine the rage of f.

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To determine the range of the function \( f(x) = \frac{x^2}{1+x^2} \) for all \( x \in \mathbb{R} \), we can follow these steps: ### Step 1: Set up the equation Let \( y = f(x) = \frac{x^2}{1+x^2} \). ### Step 2: Rearrange the equation Multiply both sides by \( 1 + x^2 \) to eliminate the fraction: \[ ...
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